风致颗粒-流体流场的数学模型及其在直升机云问题中的应用
A mathematical model for wind-generated particle-fluid flow fields with an application to the helicopter cloud problem
AI总结：
本文建立静止颗粒床上方风致两相流化云的数学模型，通过界面薄过渡层的力平衡导出宏观边界条件以封闭两相流，并用于解析与数值分析直升机褐化问题。
摘要：
我们建立了一个模型，用于描述在原本静止的颗粒床上方流动的流体与颗粒床之间的相互作用；通常情况下，颗粒会从颗粒床的上表面被夹带入流体或从流体中迁出，从而在颗粒床上方形成完全两相的流化云。该大尺度流化区域内的流动被视为两相流，而颗粒床夹带与迁出的关键过程，则通过考察完全流化区域与静止颗粒床之间界面处薄过渡层内颗粒所受的局部动力学力平衡来处理。这种细致分析导出了该界面处一个附加的宏观边界条件，从而封闭了上方主体流化区域中的两相流问题。随后，我们引入了著名的直升机褐化（brownout）问题的一个基础模型，并运用论文前半部分建立的理论，从解析和数值两方面对该模型进行了完整分析。
英文摘要：
We develop a model for the interaction of a fluid flowing above an otherwise static particle bed, with generally the particles being entrained or detrained into the fluid from the upper surface of the particle bed, and thereby forming a fully two phase fluidized cloud above the particle bed. The flow in this large scale fluidized region is treated as a two-phase flow, whilst the key processes of entrainment and detrainment from the particle bed are treated by examining the local dynamical force balances on the particles in a thin transition layer at the interface between the fully fluidized region and the static particle bed. This detailed consideration leads to the formation of an additional macroscopic boundary condition at this interface, which closes the two phase flow problem in the bulk fluidized region above. We then introduce an elementary model of the well known helicopter brownout problem, and use the theory developed in the first part of the paper to fully analyse this model, both analytically and numerically.
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